sqr(x^2-4)+(x^2)/x^2+1
I got ((x^2+1)*sqr(x^2-4)+x^2)/x^2+1
But my teacher gave (sqr(x^2-4)+x^2)/x^2+1
I did the problem over again but I can't figure out why my teacher got the answer. Can someone confirm that my teacher is right or am I right?
sqr=square root
^=to the power of
/=divided by
*=multiplied by
I get
[(x^2+1)√(x^2-4) + x^2]/(x^2 + 1)
which matches your answer.
To determine whether your answer or your teacher's answer is correct, we will simplify the expression step-by-step using the order of operations.
The given expression is:
sqrt(x^2 - 4) + (x^2 / x^2 + 1)
Step 1: Simplify the denominator
The denominator (x^2 / (x^2 + 1)) can be simplified. To do this, we need to factor out x^2 and write the expression as:
x^2 / x^2 * (x^2 + 1)
Step 2: Simplify the numerator
The numerator (sqrt(x^2 - 4)) can be simplified by factoring it out:
(sqrt(x^2 - 4)) * (x^2 + 1)
Step 3: Simplify further
Now we have:
(sqrt(x^2 - 4) * (x^2 + 1)) / (x^2 / x^2 * (x^2 + 1))
Step 4: Cancel out common factors
Notice that (x^2 + 1) appears in both the numerator and the denominator. We can cancel them out:
(sqrt(x^2 - 4) * (x^2 + 1)) / (x^2 / x^2 * (x^2 + 1))
= sqrt(x^2 - 4) / (x^2 / x^2)
= sqrt(x^2 - 4)
Therefore, the correct simplified form of the expression is sqrt(x^2 - 4). This means your teacher's answer is correct, and your initial answer, ((x^2 + 1) * sqrt(x^2 - 4) + x^2) / (x^2 + 1), is not simplified correctly.